How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery. To address this, we introduce analytically tractable Bayesian information restricted diffusion (BIRD) models, in which each pixel observes restricted information about noisy data.
arXiv:2607. 08041v1 Announce Type: new Abstract: How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery.
arXiv:2310. 05264v5 Announce Type: replace Abstract: In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often yield remarkably similar outputs.
arXiv:2606. 09718v1 Announce Type: new Abstract: Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored.
arXiv:2602. 09651v2 Announce Type: replace-cross Abstract: Diffusion models do not recover semantic structure uniformly over time.
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.
arXiv:2409. 02426v5 Announce Type: replace Abstract: Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood.
arXiv:2607. 20540v1 Announce Type: cross Abstract: How should a diffusion model decide which noise levels to train on, and how much?
arXiv:2605. 13175v2 Announce Type: replace Abstract: Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity.
arXiv:2512. 24780v2 Announce Type: replace Abstract: Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking.
arXiv:2512. 20963v3 Announce Type: replace Abstract: Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective.
arXiv:2607. 10430v1 Announce Type: cross Abstract: Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity.